Answer
a. $\bar{x}$ = 123.5, μ=120,$σ_\bar{s}$ =$ \frac{15}{$81}$, n = 81
α = 0.025 / 2 =0.0125, df = 81-1=80, critical value= 2.24
t=$ \frac{\bar{x}-μ }{σ_\bar{s}}$
= $ \frac{123.5-120 }{1.67}$
=2.1
Rejection region = z< -2.24 or z > 2.24
Non rejection region = -2.24 < z < 2.24
The value z = 2.1 falls within the non- rejection region, hence we failed to reject the null hypothesis.
b. The probability of making a Type I error : α = 0.025
c. By p value approach,
If α=0.01, .
p-value = P(Z>2.1) = 0.0179 > α
The p-value =0.0179 is larger than α , hence we failed to reject the null hypothesis.
If α=0.05, .
p-value = P(Z>2.1) = 0.0179 < α
The p-value =0.0179 is smaller than α , hence we reject the null hypothesis.
Work Step by Step
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